Using a bridged amp at 8 ohms w/a 4 ohm speaker.

I tried something similar with my Parasound 2250 V2 amp.   I used the 8-4 load setting for a 8 Ohm rated subwoofer that dropped into the 6 Ohm range.   The catch is, I had two subs in parallel so it now dropped into the 3 Ohm range.  It didn't hurt the amp but when the music dropped into the basement, the sound completely turned to mud and was rather disgusting.   Otherwise, the sound was amazingly good.   I suspect the same thing will happen in your case.   It is usually wise to follow the manufacturer's recommendations, as they do know their products better than anyone else.  

So long as you remain well short of the maximum power output, you should be safe.  However, given the impedance dips and the amplifier you may find the amplifier's output may follow the impedance curve.  In other words, it may drop where the speaker's impedance drops, and then rise back again, so it's not an ideal situation for this speaker. 

I would probably suggest that in this case, bi-ampingis a better option.  Use one side for the bass and another for the treble.  By splitting the current needed, the amp will perform more stiffly.

Try them out and report back.

FYI: In extreme cases, bridging an amp, and driving too low a speaker impedance can cause damage to the amplifier due to excess current.

+1 for bi-amping this speaker. Power hungry speaker, you'll notice a big improvement in sound. Avoid damage to the amplifier this way.